Schrodinger equation from an exact uncertainty principle

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.Comment: Latex, 18pp, nature of fluctuations & differences from stochastic mechanics clarifie

Monoid varieties with extreme properties

Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is shown that there are, nevertheless, many finite monoids that generate monoid varieties with continuum many subvarieties; these include any finite inherently non-finitely based monoid and any monoid for which $xyxy$ is an isoterm. It follows that the join of two Cross monoid varieties can have a continuum cardinality subvariety lattice that violates the ascending chain condition. Regarding monoid varieties with countably infinitely many subvarieties, the first example of a finite monoid that generates such a variety is exhibited. A complete description of the subvariety lattice of this variety is given. This lattice has width three and contains only finitely based varieties, all except two of which are Cross

On two recent proposals for witnessing nonclassical gravity

Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al. and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by explicit counterexamples based on the configuration-ensemble model. Thus, neither proposal provides a definitive test of nonclassical gravity.Comment: New references added, minor corrections. Close to final versio

Why do Gull-billed Terns Gelochelidon nilotica feed on fiddler crabs Uca tangeri in Guinea-Bissau?

Gull-billed Terns Gelochelidon nilotica wintering in Guinea Bissau mainly fed on fiddler crabs Uca tangeri and were occasionally seen feeding on fish and locusts. As fiddler crabs have a low energy content, terns need a large gross intake to meet daily energy demands. Fiddler crabs also have a low ratio of digestible flesh to exoskeleton, and therefore tern food intake may be limited by gut capacity. Activity budgets of Gullbilled Terns feeding on fiddler crabs showed that a considerable part of the time was spent resting. The duration of resting intervals increased with energy intake and was positively correlated with the metabolisable energy content of the crab eaten, suggesting that resting periods were required for a proper digestion. The poor quality of fiddler crabs was offset by high capture rates. So daily energy expenditure of the terns could easily be met by feeding on fiddler crabs. Even when resting pauses were included in foraging time, foraging for only 1.5 hours on fiddler crabs satisfied the terns&rsquo; daily energy demands. Instead, feeding on energy-rich fish would require about 2.5 hours to satisfy daily energy demands. Compared to the more specialised piscivorous Little Tern Sternula albifrons and Sandwich Tern Sterna sandvicensis, capture rate of fish was poor in Gull-billed Terns. From an energetic point of view, wintering Gull-billed Terns feeding on fiddler crabs seem to have an easy living in Guinea Bissau.<br /

Monte Carlo simulations reveal the straightening up of an end-grafted flexible chain with a rigid side chain

We have studied the conformational properties of a flexible end-grafted chain (length $N$) with a rigid side chain (length $S$) by means of Monte Carlo simulations. Depending on the lengths $N$ and $S$ and the branching site, $b$, we observe a considerable straightening of the flexible backbone as quantified via the gyration tensor. For $b=N$, i.e. when attaching the side chain to the free end of the flexible backbone, the effect was strongest

High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder

Diamond "lattices" are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, $A$ and $B$. The construction recipe for diamond graphs depends on a branching number $b\in \mathbb{N}$ and a segmenting number $s\in \mathbb{N}$, for which a larger value of the ratio $s/b$ intuitively corresponds to more opportunities for intersections between two randomly chosen paths. By attaching i.i.d. random variables to the bonds of the graphs, I construct a random Gibbs measure on the set of directed paths by assigning each path an "energy" given by summing the random variables along the path. For the case $b=s$, I propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs, and the partition function (the normalization factor of the Gibbs measure) appears to converge in law. I prove that all of the positive integer moments of the partition function converge in this limiting regime. The motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the $b<s$ case.Comment: 28 pages, 1 figur

Transformation in higher education and financial sustainability : the IFIE-concept

Published ArticleThe world today is in a period of transition. Traditional higher education institutions also seem to have lost whatever stability they may once have possessed. A failure to respond to exponential change in society affects the economic growth and the development of any enterprise. Higher educational institutions have had to make a paradigm shift; no longer can they merely systematize value (using, measuring, controlling and managing knowledge), they must now create value by formulating and producing market-driven niche products (economic value of knowledge) congruent with the existing or desired mission, vision, strategic imperatives and intrinsic nature of the institution. It is argued that the adaptive responsiveness towards the implementation of the forces arising from the synergistic effects embedded within the integration of financial and intellectual capital (entrepreneurial skills and creative ideas in the minds of people that do not form part and parcel of a service contract/job description) shaped by entrepreneurial activity (IFIE-concept) could revitalize processes and attitudes and prevent educational institutions from becoming poverty stricken academic communities - i.e., transform the institution into robust and independent academic bodies with identity, integrity and self esteem

Positive representations of finite groups in Riesz spaces

In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive $G$-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.Comment: 23 pages. To appear in International Journal of Mathematic